1. Field of Invention
The present invention relates to methods and apparatus for determining the tension in a span of material such as rope, cable, chain, belt, webbing or similar structure.
More particularly, the present invention pertains to methods and apparatus for measuring tension in a span of material using a sensor for determining the fundamental frequency of vibration in the material at points removed from mid-span of the tensioned cable.
2. Description of the Prior Art
In industrial, marine, oil field and numerous other applications, it is necessary and desirable to be able to determine and/or monitor tension in a suspended cable, chain, tubing or other elastic support so as to adjust tension to prescribed safe limits and to prevent damage or destruction due to overstressing. It is necessary, for example, to monitor the tension in electrical power conductors, tower guy wires, marine anchor chains or mooring lines, oil field tubing strings, wire rope for suspending apparatus in a well, materials used in manufacturing processes, as well as in many other applications.
Prior methods and apparatus for monitoring tension in cables or the like generally depended upon the detection of the frequency of vibrations occurring in the cable in response to mechanical or electrical perturbation and the known relationships of harmonic frequency to cable tension: EQU F=(1/2L) (T/m).sup.1/2, or EQU T=(2 LF).sup.2 m
where
T=tension in the cable; PA1 L=length of the portion of cable free to vibrate; PA1 F=the fundamental frequency of vibration of the measured length of cable; and PA1 m=linear mass density. PA1 n=the order of the harmonics; PA1 l=the length of span between two supports; PA1 T=tension; PA1 m=mass per unit length; PA1 E=modulus of elasticity of the material; and PA1 I=area moment of inertia of the material.
Such a method and apparatus was described in U.S. Pat. No. 4,158,962. Variations of this same general approach were disclosed in U.S. Pat. Nos. 2,040,874; 2,265,786; 2,618,970; 2,923,150; 3,394,587; 3,403,553; 3,540,271; 3,871,217; 3,889,525; 3,942,369; 4,376,368 and 4,393,725.
Some prior systems used acoustic sensing and amplifying devices located near the mid-span point of the cable to generate an audible tone roughly corresponding to the frequency of vibration in the cable which resulted from physically or electrically "plucking" the cable as one would pluck a guitar string. The detected and amplified tone was aurally compared and matched by the operator to a tone generated by one of a set of prestressed cables or signals of known frequency to obtain an approximation of the resonant frequency of the monitored cable. Such systems were disclosed in U.S. Pat. Nos. 2,040,874 and 2,265,786 and were inherently inaccurate. These systems as well as most other prior methods ignored the contribution of second and higher order harmonics which made them useful only where precision was unnecessary and where mid-span location of the sensor, i.e., where higher order harmonics were least significant, was feasible.
Other prior systems provided a magnetic field surrounding a suspended portion of the cable and detected the frequency of alternating current or magnetic field perturbation caused by vibrations in the cable to estimate the cable tension. Such systems were disclosed in U.S. Pat. Nos. 2,618,970; 3,871,217; 3,889,525; 3,942,369 and 4,158,962. Those systems were limited to detection of tension in conductive media or required the use of conductive sleeves surrounding a non-conductive cable. The accuracy and detector location of these systems was limited since the contribution of second and higher order harmonics was ignored and the detector had to be located near mid-span of a supported portion of the cable.
A similar method and apparatus for measuring tension was disclosed in U.S. Pat. No. 3,403,553 which used an electrical pressure transducer in contact with a vibrating portion of the suspended cable to produce an electrical signal indicative of the frequency of cable vibrations. This system attempted to improve the accuracy of the frequency detection by passing the generated electrical signal through a low pass filter to eliminate random high frequency noise. Accurate measurement using this approach was nonetheless limited to mid-span locations where the contribution of higher order harmonics was less significant. Furthermore, this system made no provision for the error introduced due to dynamic changes in the relative amplitudes of first and second harmonics where threshold crossing frequency detection was used.
In many applications, it is not feasible or practical to locate the vibration detection sensor at or near mid-span of the vibrating object. For example, where a cable or chain is stretched over an expanse of water as is often encountered in offshore drilling, anchoring and mooring applications and in other such situations where access to a mid-span location is not practical. Moreover, it is generally desirable in most applications to locate the sensor near one end or the other of the cable to avoid creating physical obstructions that are a nuisance and at times a safety hazard.
In prior methods, tension was measured by reference to the resonant or natural frequency of vibration detected in the cable in accordance with the relationship between tension and frequency set forth above. All prior methods based the computation of tension upon measurement of the fundamental or first harmonic of the transverse vibration in the cable without disclosing an effective method of extracting the fundamental from the composite wave form which includes higher order harmonics. Thus, prior systems were not well suited for use with velocity or acceleration type detectors having frequency response characteristics which are greatly influenced by the presence of second and higher order harmonics.
There are numerous simultaneous, harmonically related, transverse vibration frequencies in the composite wave form that relate to tension according to the formula: ##EQU1## where f=transverse vibration frequency;
In prior methods, the sensor was located near mid-span of the cable to enable detection of the first or fundamental harmonic. Reference to FIG. 1 illustrates why this was feasible. The fundamental frequency or first mode is clearly the largest component of the composite waveform when measured near the mid-point. As one moves toward either end, however, the ratio of amplitude of the fundamental harmonic to those of higher order harmonics becomes progressively less. Thus, prior art methods which did not provide an effective means for extracting the fundamental frequency from the other harmonics necessarily were only useful if detection was at or near mid-span.
Generally speaking, three fundamental types of vibration sensors are feasible. These are acceleration sensors, velocity sensors and displacement sensors.
Displacement sensors, such as an electromechanical transducer detect amplitude of displacement in the cable and produce an analog output signal that is proportionate to the amplitude of the composite waveform in the cable, i.e., the summation of the amplitudes of all the harmonics at the location of the sensor.
A velocity sensitive transducer produces an output analog signal proportionate to the summation of the velocities of the various harmonics at the sensor location. Since velocity is directly proportional to frequency with amplitude constant, the output level of a velocity sensor increases with frequency. Thus, a doubling of the frequency, an octave, results in a doubling of the amplitude of the sensor output or a six decibel increase when the frequency response is plotted on a logarithmic scale. Consequently, the output corresponding to the second harmonic will have an amplitude which is amplified by two relative to the fundamental, the fourth harmonic by four, etc. Thus the composite output of the velocity sensor rapidly becomes rich in harmonics as the sensor is moved away from mid-point on the span and it becomes increasingly more difficult to detect the fundamental.
An acceleration sensitive transducer produces an output which is proportionate to the summations of the acceleration of the several harmonics at the sensor location. Since acceleration is the rate of change in velocity, an acceleration sensor will produce an output which quadruples in amplitude with each doubling in frequency. In other words, its frequency response plotted on a logarithmic scale increases at the rate of twelve decibels per octave. Thus, the output corresponding to second harmonic amplitude is amplified by four relative to the fundamental, fourth harmonic output by sixteen, etc., making the location of an acceleration sensor heretofore at any point other than mid-span highly undesirable.
A more subtle, deleterious, summing effect results from sensing the composite signals. The second harmonic adds an offset or bias to the composite. The magnitude of the offset is proportionate to the amplitude of the second harmonic. The relative amplitudes of the fundamental and second harmonic, shown in FIG. 1 for example, exist only momentarily, immediately after excitation. Since damping is proportional to velocity, the higher frequency components, i.e., the second harmonic, will decay faster than the fundamental, thereby changing the relative amplitude of the second and fundamental harmonics and thus the appropriate offset or bias level. This shifting produces error, especially if threshold crossing is used to convert frequency to voltage.